The present paper modifies and studies jumping finite automata so they always perform two simultaneous jumps according to the same rule. For either of the two simultaneous jumps, it considers three natural directions---(1) to the left, (2) to the right, and (3) in either direction. According to this jumping-direction three-part classification, the paper investigates the mutual relation between the language families resulting from jumping finite automata performing the jumps in these ways and the families of regular, linear, context-free, and context-sensitive languages. It demonstrates that most of these language families are pairwise incomparable---that is, they are not subfamilies of each other and, simultaneously, they are not disjoint.